I’ve said it before and will say it again: Björk is the best thing to happen to contemporary music theory education. No matter what weird scale you’re trying to teach, she’s used it in a catchy, memorable tune. “Possibly Maybe” uses two weird scales: Lydian mode, in the A section (the verses), and melodic minor scale, in the B section (the “chorus” and the long outtro).
The B Lydian mode is almost the same as the B major scale, with one crucial difference: while the B major scale’s fourth note is E, B Lydian mode has E-sharp (enharmonically F natural) instead. That E-sharp changes the feeling of the scale from the plain vanilla of major to a more floating, dreamlike feeling. Try switching back and forth between B Lydian and B major to hear the difference.
The keyboard part under the verses of “Possibly Maybe” never actually uses the E-sharp that characterizes the Lydian mode. But that note is present throughout the vocal melody, and if you try improvising around on the scale, you’ll hear how the E-sharp fits in.
The first two notes are B, the root, and A-sharp, the seventh scale degree. In Western tonal theory, the seventh functions as the “leading tone,” the note that pulls strongly up to the root. But in modal music, the seventh is just another scale tone, another color in the palette. In “Possibly Maybe” it feels more like the root is pulling you down to the seventh.
The next three notes in the riff are D-sharp, F-sharp, and A-sharp, which together make a D# minor chord. However, they have another relationship too. If you take these notes and put B underneath them, you get an Bmaj7 chord. Even without the B present, your ear still detects the major seventh chord structure. This minor-major ambiguity combines with the syncopated rhythm to give the riff its sophisticated, jazzy intrigue.
The chorus riff uses the same rhythm and general melodic shape, but a very different scale, for a very different mood: C-sharp melodic minor.
There are a lot of different minor scales. Melodic minor is the most exotic one. It only differs from the major scale in one note, the third scale degree. In C-sharp major, the third note is E-sharp. In C-sharp melodic minor, it’s E natural. This all may not seem so strange on paper, but it sounds arrestingly weird. The A-sharp and B-sharp (enharmonically C natural) are characteristic of major, and in the minor-key context, they’re otherworldly. There’s a tritone between E and A-sharp, and another one between F-sharp and B-sharp. That’s twice as many tritones as a “normal” Western scale would have. Melodic minor is most frequently used in highbrow jazz, by the likes of John Coltrane and Miles Davis. It’s vanishingly unusual in pop–here’s the most complete list of usages that I’ve been able to find.
The keyboard riff from the B section of “Possibly Maybe” begins with C-sharp, the root, A-sharp, the major sixth, and E, the minor third. That establishes the melodic minor mood completely in just three notes, including that A-sharp to E tritone. The riff concludes with G-sharp, the fifth, and then ends on A-sharp again, hammering that note home. Once again, it’s a lot of jazzy harmony packed into a tiny phrase.